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### 2D-1D dimensional reduction in a toy model for magnetoelastic interactions

Applications of Mathematics

The paper deals with the dimensional reduction from 2D to 1D in magnetoelastic interactions. We adopt a simplified, but nontrivial model described by the Landau-Lifshitz-Gilbert equation for the magnetization field coupled to an evolution equation for the displacement. We identify the limit problem by using the so-called energy method.

### A frictional contact problem with wear and damage for electro-viscoelastic materials

Applications of Mathematics

We consider a quasistatic contact problem for an electro-viscoelastic body. The contact is frictional and bilateral with a moving rigid foundation which results in the wear of the contacting surface. The damage of the material caused by elastic deformation is taken into account, its evolution is described by an inclusion of parabolic type. We present a weak formulation for the model and establish existence and uniqueness results. The proofs are based on classical results for elliptic variational...

### A quasistatic contact problem with unilateral constraint and slip-dependent friction

Applicationes Mathematicae

We consider a mathematical model of a quasistatic contact between an elastic body and an obstacle. The contact is modelled with unilateral constraint and normal compliance, associated to a version of Coulomb's law of dry friction where the coefficient of friction depends on the slip displacement. We present a weak formulation of the problem and establish an existence result. The proofs employ a time-discretization method, compactness and lower semicontinuity arguments.

### A thermodynamic approach to nonisothermal phase-field models

Applicationes Mathematicae

The goal of this paper is to work out a thermodynamical setting for nonisothermal phase-field models with conserved and nonconserved order parameters in thermoelastic materials. Our approach consists in exploiting the second law of thermodynamics in the form of the entropy principle according to I. Müller and I. S. Liu, which leads to the evaluation of the entropy inequality with multipliers. As the main result we obtain a general scheme of phase-field models which involves an...

### An elastic Green matrix for a semistrip.

Bulletin of TICMI

### Applications of a weighted symmetrization inequality to elastic membranes and plates.

Journal of Inequalities and Applications [electronic only]

### Asymptotic analysis of an approximate model for time harmonic waves in media with thin slots

ESAIM: Mathematical Modelling and Numerical Analysis

In this article, we derive a complete mathematical analysis of a coupled 1D-2D model for 2D wave propagation in media including thin slots. Our error estimates are illustrated by numerical results.

### Asymptotics of the energy functional for a fourth-order mixed boundary value problem in a domain with a cut.

Sibirskij Matematicheskij Zhurnal

### Boundary controllability of a chain of serially connected Euler-Bernoulli beams with interior masses.

Collectanea Mathematica

### Characterization of the limit load in the case of an unbounded elastic convex

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this work we consider a solid body $\Omega \subset {ℝ}^{3}$ constituted by a nonhomogeneous elastoplastic material, submitted to a density of body forces $\lambda f$ and a density of forces $\lambda g$ acting on the boundary where the real $\lambda$ is the loading parameter. The problem is to determine, in the case of an unbounded convex of elasticity, the Limit load denoted by $\overline{\lambda }$ beyond which there is a break of the structure. The case of a bounded convex of elasticity is done in [El-Fekih and Hadhri, RAIRO: Modél. Math. Anal. Numér. 29 (1995)...

### Characterization of the limit load in the case of an unbounded elastic convex

ESAIM: Mathematical Modelling and Numerical Analysis

In this work we consider a solid body $\Omega \subset {ℝ}^{3}$ constituted by a nonhomogeneous elastoplastic material, submitted to a density of body forces $\lambda f$ and a density of forces $\lambda g$ acting on the boundary where the real $\lambda$ is the loading parameter. The problem is to determine, in the case of an unbounded convex of elasticity, the Limit load denoted by $\overline{\lambda }$ beyond which there is a break of the structure. The case of a bounded convex of elasticity is done in [El-Fekih and Hadhri, RAIRO: Modél. Math. Anal. Numér. 29 (1995)...

### Dynamical model of viscoplasticity

This paper discusses the existence theory to dynamical model of viscoplasticity and show possibility to obtain existence of solution without assuming weak safe-load condition.

### Existence and uniqueness for the three-dimensional thermoelasticity system in shape memory problems

Banach Center Publications

A thermodynamically consistent model of shape memory alloys in three dimensions is studied. The thermoelasticity system, based on the strain tensor, its gradient and the absolute temperature, generalizes the well-known one-dimensional Falk model. Under simplifying structural assumptions we prove global in time existence and uniqueness of the solution.

### Existence, blow-up and exponential decay for a nonlinear Love equation associated with Dirichlet conditions

Applications of Mathematics

In this paper we consider a nonlinear Love equation associated with Dirichlet conditions. First, under suitable conditions, the existence of a unique local weak solution is proved. Next, a blow up result for solutions with negative initial energy is also established. Finally, a sufficient condition guaranteeing the global existence and exponential decay of weak solutions is given. The proofs are based on the linearization method, the Galerkin method associated with a priori estimates, weak convergence,...

### Existence of pullback attractors for the coupled suspension bridge equations.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### Exponential decay to partially thermoelastic materials

Bollettino dell'Unione Matematica Italiana

We study the thermoelastic system for material which are partially thermoelastic. That is, a material divided into two parts, one of them a good conductor of heat, so there exists a thermoelastic phenomenon. The other is a bad conductor of heat so there is not heat flux. We prove for such models that the solution decays exponentially as time goes to infinity. We also consider a nonlinear case.

### Exponential stability and global attractors for a thermoelastic bresse system.

Advances in Difference Equations [electronic only]

### Global well-posedness and blow up for the nonlinear fractional beam equations

Applicationes Mathematicae

We establish the Strichartz estimates for the linear fractional beam equations in Besov spaces. Using these estimates, we obtain global well-posedness for the subcritical and critical defocusing fractional beam equations. Of course, we need to assume small initial data for the critical case. In addition, by the convexity method, we show that blow up occurs for the focusing fractional beam equations with negative energy.

### Initial-boundary value problems for quasilinear dispersive equations posed on a bounded interval.

Electronic Journal of Differential Equations (EJDE) [electronic only]

### Iteratively solving a kind of Signorini transmission problem in a unbounded domain

ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique

In this paper, we are concerned with a kind of Signorini transmission problem in a unbounded domain. A variational inequality is derived when discretizing this problem by coupled FEM-BEM. To solve such variational inequality, an iterative method, which can be viewed as a variant of the D-N alternative method, will be introduced. In the iterative method, the finite element part and the boundary element part can be solved independently. It will be shown that the convergence speed of this iteration...

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